In an agitator mill of this type known from U.S. patent application Ser. No. 07/439,048, now U.S. Pat. No. 5,062,577, the auxiliary grinding bodies are centrifuged off the flow of grinding stock and auxiliary grinding bodies via bypasses, before it reaches the separator device. In this case the separator device only has the function of collecting worn-out auxiliary grinding bodies that are too light in weight to be directly catapulted off through the bypasses, and of serving as a throttle to build up a counterpressure working against the flow of grinding stock. As a rule the agitator element is provided with agitator implements projecting in the form of pegs into the exterior grinding chamber or the interior grinding chamber, respectively. Stationary agitator implements are in like manner arranged on the grinding receptacle and project into the exterior grinding chamber, and equally on the interior stator and project into the interior grinding chamber. In this case no stationary agitator implements are arranged on the interior stator in the area ahead of the bypasses so as to ensure the centrifuging off of the auxiliary grinding bodies via the bypasses.